Computational Fluid Dynamics

Transcription

1 Computational Fluid Dynamics OF TURBULENCE EFFECTS ON THE SEABED For the degree of Bachelor of Science MARCH 2015

2 Table of Contents List of Figures and Tables... III Abstract... V Nomenclature... VI 1 Introduction Background Motivation Purpose of Dissertation Subsea Cable Software Theory Literature Review. Best Practice Hydrodynamic Flume Experiment Seabed profile Scaling laws Seabed Construction Experiment Methodology CFD Process Design Modeller ANSYS Meshing CFX-Pre: Boundary Conditions Main solver Results Experimental data CFD data Validation Assumptions and Limitations Guidelines Further work Conclusion II

3 13 Bibliography A. Appendix A Scaling laws... A B. Appendix B Experimental data graph... B C. Appendix C - Experiment and CFD data... J LIST OF FIGURES AND TABLES Figure Cable parameters and cable routing. Source: Industrial Partner (2015) Figure 5-1 Pentland Firth, Scotland - site bathymetry profile. Source: University (2014)... 8 Figure 5-2 Pentland Firth, Scotland - bathymetry profile Rhinoceros screenshot Figure 5-3 Site bathymetry profile... 9 Figure 5-4 Bathymetry construction process Figure 5-5 Seabed sections CAD Figure 5-6 Seabed sections - construction site Figure 5-7 Vectrino Profiler Figure 5-8 Velocity recorded at small area Figure 6-1 Design Modeller computational domain Figure 6-2 Computational domain mesh Figure 6-3 Computational domain mesh - cross section view Figure 6-4 Boundary Conditions in CFX-Pre Figure 7-1 Velocity vs. motor power Figure 7-2 Vertical inlet velocity profile Figure 7-3 Velocity profile across the whole domain Figure 7-4 Velocity profile across the whole domain - zoom in Figure 7-5 Velocity profile for the computational domain Figure 7-6 Vector velocity plot - CFD Figure 7-7 Velocity variation 5mm above seabed - CFD Figure 8-1 Experimental and CFD data comparison: κ-ɛ Figure 8-2 Experimental and CFD data comparison: κ-ω SST Figure 8-3 Experimental and CFD data comparison: RSM SMC-BSL Figure 8-4 Residual sum of square - eddy length scale 35mm Figure 8-5 Residual sum of square - eddy length scale 25mm Figure 8-6 Residual sum of square - eddy length scale 15mm FigureB 1Full scale X-axis velocities... B III

4 FigureB 2Full scale Y-axis velocities... C FigureB 3 Full scale Z-axis velocities... D FigureB 4 Full scale RMS turbulence fluctuation... E FigureB 5 RMS turbulence fluctuation - individual axis... F FigureB 6 Signal-Noise Ratio... G FigureB 7 Data quality... H FigureB 8 Data correlation... I Table 1 Validation points location TableC 1 Experimental and CFD data - κ-ɛ model... J TableC 2 Experimental and CFD data - κ-ω SST model... K TableC 3 Experimental and CFD data - RSM SMC-BSL model... L IV

5 ABSTRACT Subsea cables fatigue and cable stability have been identified as main areas of concern for marine renewable energy projects, therefore smart routing tools need to be developed to optimize the cable routing, considering the sheltering effects of the seabed. The industrial partner has developed a subsea cable software featuring cable route analysis and optimisation with Computational Fluid Dynamics (CFD) integration. In this report turbulence modelling on the seabed is analysed in order to validate a turbulence model which needs to be used for flow simulation as input in the cable software. Using real data from Pentland Firth, a seabed profile was built and scaled down using Froude similarity to a ratio of 1/50. Experimental tests were carried out to record velocity field data above the seabed over a sampling volume of 35mm at 100Hz. An ANSYS CFX model was designed to anayse the effect of κ-ɛ, κ-ω SST and RSM SMC-BSL turbulence models and parametric studies have been conducted to show the effect of various turbulence length and intensity for each of the turbulence model. A validation methodology using the equivalent residual sum of square (RSQ-eq) was used to quantify the discrepancy between data. The main results are as follows: i). The bathymetry plays a significant role in defining the fluid flow; ii). A similar pattern was identified in terms of discrepancy of data for all three models, but the κ-ω SST has the lowest RSQ-eq; and iii). For each turbulence length considered, the data shows a similar pattern and it has very tiny variation for each turbulence model and intensity rate. The report ends with the limitations involved, guidelines for other users and potential further work. V

6 NOMENCLATURE BC - Boundary Conditions CFD - Computational Fluid Dynamics CNC - Computer (or computerized) Numerical Control DECC Department of Energy and Climate Change DES Detached Eddy Simulation DNV - DET NORSKE VERITAS GUI Graphical User Interface GW gigawatts NS Navier-Stokes NURBS Non-Uniform Rational B-Splines PDE Partial Differential Equation RANS - Reynolds-averaged Navier-Stokes Re Reynolds number RSM-SMC-BSL Reynolds model Second Moment Closure Baseline RSQ-eq equivalent of Residual Sum of Square SNR Signal to Noise Ratio SST Shear Stress Transport T i Turbulence Intensity T L Turbulence Length VP Vectrino Profiler VI

7 1 INTRODUCTION 1.1 Background Turbulence is generally considered as one of the unsolved phenomena in physics which clearly means that has not yet been discovered only one turbulence model, which describes its appearance and maintenance and it could be applicable in all situations. Over the last few decades, engineers and scientists worked together to develop turbulence models to describe best the turbulence effects for various applications, but many challenges are still to be addressed. In offshore renewables projects, where burial of the power cables is not possible, turbulence on the seabed becomes of significant importance. The challenge for the developer is to successfully install the cables on a rocky seabed and to maintain the reliability over their lifetime in these harsh marine environments. Before the installation itself, careful consideration in terms of routing needs to be done. The bathymetry profile plays a significant effect on the fluid flow direction and magnitude and the sheltering effects of the bathymetry receive a key focus. If these are not considered, more costly fastening options would need to be implemented (e.g. rock bags). The less fluid interaction over the cable, the more increase in the factor of safety, therefore an increase in reliability and safety and decrease in maintenance and cost. The main areas of concern for marine renewable energy projects are challenges around subsea cables fatigue and cable stability. Due to hydrodynamic loads, the exposed areas of the cable can experience continual movement, which could cause mechanical fatigue on the cable component. It is therefore essential to design an effective way to minimize movement and vibration and to specify suitable means of mitigating potential risk. External protection measures could be applied, but by optimizing the cable routes the challenge could be partly optimized (Wind Energy Network, 2013). Another important consideration is the interraction between the cable and the (erodible) seabed. Mao (1986) and Jensen, et al. (1990) have studies the scour features such as size and scour hole and time scale of scour formation, showing that the scour develops with space and time, the mean flow field and turbulence around and the forces on the pipeline undergo considerable changes. In this context, the need for cable route optimisation in order to minimise such effects is critical. To remain cost-effective, the cable stability needs to be optimised via means of intelligent, smart routing tools. The software tools could be optimised and further validated as more information becomes available so the marine industry could benefit from these tools in similar ways as the wind industry benefits from software such as Bladed. To further emphasize the importance of the tool, dynamic loads could be exported from the tool and used in other facilities such as Dynamic Marine Component Test rig (DMaC) for mechanical tests. 1

8 1.2 Motivation The UK benefits from valuable offshore, both wind and wave and tidal resource and it is committed to decarbonize the energy sector using green technologies. The UK Renewable Energy Roadmap indicates a possible range of up to 18GW for the deployment of offshore wind by With substantial reduction in costs, there is an even higher potential for further deployment after 2020 with over 40GW possibly by 2030 (DECC, 2011). Wave and tidal stream has the potential to meet up to 20% of the UK s current energy demand with an installed capacity of 30-50GW. According to DECC (2011), between 200 and 300MW of generating capacity may be able to be deployed by 2020 with an an additional deplyment of up to 27GW by Considering only the potential deployment for offshore wind, this would equate to further 10,000-15,000km of export cables and over 5,000km of array cables (Red Penguin, 2012). This figure will increase even more when more certain scenarios of wave and tidal energy deployments come into play. One way of cost reduction could be achieved by developing smart tools for subsea cable routing taking the advantage of the natural sheltering effects of the seabed. At the current state, the industry does not follow any guideline in terms of smart routing as this is not existent. The current route selection methodology is mainly done in terms of installation easiness, considering other parameters such as environmental and archeological issues and a visual representation of the bathymetry and its engineering implications. 1.3 Purpose of Dissertation This project focuses particularly on the turbulence effects on the seabed with the main aim to validate experimental results with a numerical turbulence model which is meant to be used when velocity fields are generated and used as input in a cable stability tool developed by the industrial partner (Section 2). Using real bathymetry geo-reference data, a seabed profile was created using CNC router machine and casting methods, being scaled down to a scale ratio of 1/50 according to Froude scaling law. Using real averaged flow data measured at Pentland Firth, an experiment was conducted in a hydrodynamic flume to record fluid velocities close to the seabed with a Vectrino Profiler (VP)(Section 5). The experimental data will then be analyzed and compared against numerical data which is generated with computational methods using ANSYS CFX software (ANSYS, 2015). Various simulations are carried out using different turbulence models (κ-ɛ, κ-ω SST and RSM-BSL), intensity (T i) and length (T L) (Section 6). The main tool to compare the results was the RSQ-eq between the recorded and simulated data. This value is then compared and plotted against different settings; sensitivity analysis is carried out for specific T L values (Section 8). 2

9 Based on writer s experience and other sources, limitations and guidelines are then drown for each major part of the project (Section 9-10). 2 SUBSEA CABLE SOFTWARE The industrial partner has developed a unique software tool to optimize subsea power cable routes. Designed around a revolutionary cable analysis methodology, the tool combines the hydrodynamic properties with the bathymetry profile to assess the cable stability. Using multiple iterations, the tool provides an optimum route within the pre-set requirements with different routing options. The tool s features are: Cable Route Analysis Cable Route Optimisation CFD integration RPL Reporting Factor of Safety Analysis GIS Integration Figure Cable parameters and cable routing. Source: Industrial Partner (2015). 3

10 Having the option of importing the seabed geometry, cable parameters and hydrodynamic properties, the tool is generating useful insight for cable routing. The writer has been involved with the CFD integration and this is where the focus of this project is. In order to have a reliable output, the input needs to be valid. This project is designed to validate a turbulence model suitable for the data imported as hydrodynamic property. The software allows importing advanced CFD velocity fields to show velocity current at or offset from the seabed. The actual report could be taken further to produce best practice for CFD modelling as input for this tool. Having specific guidelines, the tool would be easier to be used by both experienced and unexperienced CFD users. 3 THEORY According to Hinze, the turbulence is defined as an irregular condition of flow in which the various quantities show a random variation with time and space coordinates, so that statistically distinct average values can be discerned (Wilcox, 2010). The origin of turbulence rests in small perturbations imposed on the flow. At low Reynolds numbers (Re) such disturbances are damped out by the fluid viscosity and the flow remains laminar, but at high Re they can grow and propagate, giving rise to the chaotic phenomena perceived as turbulence (Levicky, n.d.). Turbulence tends to occur from the transition from laminar to turbulent flow and it retains many of the characteristics of the transition process that created it (Baumert, et al., 2005). At the heart of any CFD code are the governing laws of the fluid flow. These are based on the fundamental laws of physics and include the mass conservation and momentum and energy equations. The continuity and momentum equations are critical for describing the motion of viscous fluid substances and they form the Navier-Stokes equations (NS-eq) where four unknowns need to be solved using partial differential equations (PDE): velocity components and pressure. Due to their complexity, these cannot be solved analytically, therefore they require numerical methods. The computational power cannot cope with every fluctuation in the flow modelled by NS-eq, therefore Reynolds introduced the most used time-averaged value of the fluid fluctuation in a new set of equations called Reynolds Average Navier-Stokes equations (RANS). As a result of Reynoldsaveraging, six unknown quantities were added, but unfortunately no additional equations were gained. In essence, Reynolds averaging is a brutal simplification that loses much of the information contained in the NS equation. The function of turbulence modelling is to devise approximations for the unknown correlations in the terms of flow properties that are known so that a sufficient number of equations exist (Wilcox, 2010). In order to be able to compute turbulent flows with RANS equations, it is necessary to develop turbulence models to predict the Reynolds stresses and the scalar transport terms. In this way the system of mean flow equations will be closed and solutions could be found. 4

11 The most known and used standard turbulence models are the two-equation models (κ-ɛ and κ-ω are the most common in most engineering equations), Reynolds models and non-rans models. The κ-ɛ model develops two PDEs for turbulent kinetic energy (κ) and dissipation rate (ɛ). The idea is to derive the exact equation for epsilon and to find suitable closure approximations. In CFX, this model uses the scalable wall-function approach to improve robustness and accuracy when the nearwall mesh is very fine. The scalable wall function allow solution on arbitrarily fine near wall grids, which is a significant improvement over standard wall functions (ANSYS CFX, 2013). Nonetheless, this model it is not suitable for boundary layer separation or flow over curved surfaces because it predicts the onset of flow separation too late and under-predicts the amount of separation later on (ANSYS CFX, 2013). One of the advantages of the κ-ω formulation is the near wall treatment for low Re where it is more accurate and more robust, it does not involve the complex nonlinear damping functions required for the κ-ɛ model and it allows for smooth shift from a low Re form to a wall function formulation. κ-ω based on Shear Stress Transport (SST) is designed to give accurate prediction by the inclusion of transport effects into the formulation of the eddy-viscosity and it is therefore recommended for high accuracy boundary layer simulations. This accounts for the transport of the turbulent shear stress and gives highly accurate predictions of the onset and the amount of flow separation under adverse pressure gradients (ANSYS CFX, 2013). Reynolds-stress models (RSM) use a different method to close the Reynolds stresses. In flows where the turbulent transport or non-equilibrium effects are important, the eddy-viscosity assumption is no longer valid and results of eddy-viscosity models might be inaccurate. These include the effects of streamline curvature, sudden changes in the strain rate, secondary flows or buoyancy. The convergence of these models may be slower and it produces unsteady results, where two-equation models give steady state solutions. In practice, the models show that they are not superior to twoequation models (ANSYS CFX, 2013). Other non-rans models include Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS). LES is an intermediate form of turbulence calculations which focuses on the behavior of the large eddies and rejects the smallest ones and it started to address problems with complex geometry. These approaches require fine grids and small timesteps, therefore are more computational demanding, but can provide details on the structure of turbulent flows which cannot be obtained from a RANS formulation. DNS is mainly used in research for basic flows due to the huge computational demand. This method considers all turbulent fluctuations and uses spatial grids that are sufficient to solve Kolmogorov length scale at which energy is dissipated (Versteeg & Malalasekera, 2007). 5

12 4 LITERATURE REVIEW. BEST PRACTICE Various literature has been published on the numerical modelling of turbulence on topics like wave and current interaction, modelling the tidal regime and more on scour effects on the seabed including subsea pipelines. To some extent, experimental data is available and the numerical simulations are validated against it. In terms of turbulence modelling for offshore cables, limited studies are available. Wave and current interaction are the most complex scenarios for subsea engineering and it is here where the biggest challenge lies. Based on previous studies and experimental data, Teles, et al. (2013) have analysed this interraction using κ-ɛ, κ-ω and the Reynolds SST turbulence model. Laboratory experiments in the flume were conducted with rough and smooth beds and the results show that the waves have a significant impact on the horizontal mean velocity. Comparing numerical results with the experimental data, good agreement is found for all turbulence models. This study was conducted on a flat bed, therefore the flow is less turbulent when compared with a bathymetry profile. Shen (n.d.) investigated the seabed stress around subsea pipelines. An experiment was conducted where DES κ-ω SST turbulence model was chosen against others due to its outstanding near wall treatment and improvemnets in ANSYS Fluent software. In analyzing the scour gap effect of unsteady flow around a pipe, Ali, et al. (2014) produced a sensitivity analysis of eleven cases of different turbulence models. Interestingly, of all turbulence models, standard κ-ɛ gives better predictions for the velocity profile when compared with the experimental data. The study shows that κ-ω models shows higher discrepancy. Turbulence closure models are assessed for tidal energy resource in Orkney by Baston, et al. (n.d.). The κ-ɛ model was used with the algebraic model, testing whether κ-ɛ results would be worse than algebraic ones, but the results are inconclusive in this respect. Other study on sediment modeling in eastern English Channel shows good agreement between the numerical and measured data. The turbulence generated at the seabed is modeled by standard κ-ɛ model (Chapalain & Thais, 2000). κ-ɛ turbulence model is also used to study the effect of wave-induced seabed response around the wind turbine foundation (Chang & Jeng, 2014), but in order to successfully capture the pressure gradients, the κ-ω approach proved to perform better (Melling, et al., n.d.). Considering the previous studies, the default κ-ɛ turbulence model seems to provide satisfactory results. Some studies show that the κ-ω model performs better for describing the flow separation. As presented above, there is discrepancy in terms of the performance of each model and this tends to be site specific and related to the physical boundaries of each system. Nonetheless, there is much more need for further investigation particularly in the area of offshore cables. Studies need to be carried out using bathymetry profiles instead of flat beds and making a through sensitivity analysis for different turbulence models and closure coefficients. 6

13 DNV (2014) has developed recommended practice for various marine operations and subsea engineering applications. In terms of cable routing, generous guidelines is given for conceptual design and various surveys, but limited information is provided in terms of sheltering effects of the seabed and turbulence modelling. In terms of the environmental conditions, the guidelines provide design for current field velocity and wave modelling, with the minimum best practice recommended to be the linear theory (DNV, 2010). With respect to turbulence intensity T i, if no other information is available, T i value of 5% is recommended and for macro-roughness areas, the value is 20-40% higher than flat areas (DNV, 2006). Furlepa (2015) recommends an average T i of 10% in tide sites and κ-ω as initial turbulence model. 5 HYDRODYNAMIC FLUME EXPERIMENT This section outlines the experiment procedure, including details on data used as input, methodology for creating the surface, scaling and instrumentation. 5.1 Seabed profile Point cloud bathymetry data from Pentland Firth was used to build the seabed profile. It is essential to develop a bathymetry selection criteria in order to select a small area which will be used for scaling the model. The following considerations are important: It is good to have a wide representation of the seabed elevation in order to have significant velocity change. This could provide more insight into the turbulence around different features. Due to the wall-bounded flow, the developed flow is likely to be in the centre of the seabed profile. Hence, this area must satisfy the criterion above. For more precise experimental results, the scaling factor is desirable to be small. The maximum velocity in the flume is 1 m/s which needs to be reflected by the scaling factor and The scaling factor needs to reflect the physical capability of CNC machine used. Its maximum drilling length is 10cm, therefore the scaled surface variation must not exceed this value. Figure 5-1 displays the bathymetry profile of the Meygen site and Figure 5-2 shows the profile of the highlighted area in Figure 5-1. The area highlighted offers wide range of features and is close to the proposed site for the turbines, therefore it was considered for the screening process. Considering the criteria above, many iterations were made to find a suitable site, with the final one in Figure 5-3. The bathymetry profile was created with the CAD software Rhinoceros. RhinoTerrain plugin was used to generate a mesh from the point cloud and Resurf plugin was used to create the surface from the mesh. The mesh is converted into NURBS curves which are defined by degree, control points, knots and evaluation rule. 7

14 Figure 5-1 Pentland Firth, Scotland - site bathymetry profile. Source: University (2014) Figure 5-2 Pentland Firth, Scotland - bathymetry profile Rhinoceros screenshot. 8

15 Figure 5-3 Site bathymetry profile 5.2 Scaling laws An experimental model needs to be conducted at the same conditions as the full one which would require similarity at different levels: geometric, kinematic and dynamic. The similarity laws are applied considering the limitations of the CNC machine, flume velocity and its physical dimensions. For the geometric similarity, the main parameters are the depth of the water and the surface variation; the selected variables give a scaling ratio of 50. In terms of kinematic similarity, equality in Reynolds number will ensure that viscous forces are correctly scaled whereas equality in Froude number will ensure that gravity forces are correctly scaled. For various reasons the similarity requirements posed by the Froude and Reynolds numbers can typically not be satisfied simultaneously. It is then necessarily to identify the dominant force according to which the scale must be done. Because the gravity forces are dominant, the Froude number was used which scaled the velocity from 2.25m/s to 0.32m/s. Full scaling methodology is presented in Appendix A. 5.3 Seabed Construction The 3D CAD model was exported as STL drawing file from computer to CNC milling machine to create the negative shape of the profile in blue foam. The construction process is presented in Figure 5-4. Initially the profile was built out of plaster, but this started to dissolve in water, therefore another model had to be rebuilt using postcrete. Additional wood-support structure was added to the bathymetry in order to make the installation easier and safer and before the bathymetry itself, a transition area was built, connecting it to a plain area which is followed by a ramp. These woodstructures were added to help the flow become more developed before it enters the bathymetry area. 9

16 The plywood and battens were covered by water-seal solution to prevent the water penetrate in the material (Figure 5-5; Figure 5-6). Figure 5-4 Bathymetry construction process 10

17 Figure 5-5 Seabed sections CAD Figure 5-6 Seabed sections - construction site 5.4 Experiment Methodology The flume is about 9m long, 0.6m wide and 0.6m high and allows a maximum water velocity of 1m/s. Before the water enters in the flume, a honeycomb makes the flow relatively steady. In terms of instrumentation, a traverse system and a VP were used. The traverse system is used to move the VP within the flume in three dimensions. The traverser can be controlled by a software application that logs the exact time-stamped position of the instruments to an accuracy of ±0.05 mm in both vertical and horizontal axes (HR Wallingford, 2014). The VP (Figure ) provides three-component velocity observations with a resolution as fine as 1mm over a 3.5cm range with an output rate as fast as 100Hz. Simultaneously, it can measure the distance to the bottom at rates of up to 10Hz by interleaving bottom detection and velocity profiling (Nortek As, 2013). 1 The developer configuration picture is from an older version of VP. 11

18 Figure 5-7 Vectrino Profiler Before the experiment, a local home was set for the bathymetry profile. This is useful to be set as a reference for the home position (0,0,0) of the Vectrino. The water in the flume was filled to the maximum (0.6m) and filtered from particles for about 20min at 60% motor power. It is important to have a developed flow before the experiment; the flume run for a few minutes before the data started to be recorded. Suction cups and widges were used to fix the bathymetry profile to the flume so it will not move. The traverse system was tested before use to make sure that it follows all points of interest. An important consideration for the VP are the weak spots which cause uncertainty in data. To avoid these, the velocity range for the instrument was chosen accordingly. The initial set of data was recorded in order to find the relationship between the motor power and the mean velocity (Figure 7-1). Additionally, horizontal and vertical profiles were recorded on the flat area before the bathymetry to be used as input data in the CFD model. A set of data was recorded across the whole area with 5cm resolution and additional data was recorded for a smaller area with the highest resolution of the VP (6mm diameter) (Figure 5-8). Figure 5-8 Velocity recorded at small area The data was recorded over a 35mm range and the main values are the 3D velocity, bottom distance, SNR, data quality etc. Other parameters (such as T i) could be easily calculated using the original 12

19 data. In order to validate the recorded data with the numerical one, a set of points were selected and the velocity associated with them was compared against the other cases. The RSQ-eq was calculated to quantify the difference between the data. 6 CFD PROCESS ANSYS Workbench links various software packages that are included in the ANSYS software suite in one, simple interface. This allows interconnectivity within different elements of the project, such as sharing the initial geometry or mesh for numerous models and then collating the results into one window. Another advantage of the software is the ability to conduct parametric what-if analysis. 6.1 Design Modeller Design Modeller can be used to import geometry from different formats into the ANSYS Workbench software suite and adjust it so that it is in suitable format for CFD simulation. Initially, the whole area of the bathymetry was imported, but due to computational limitations, after iterative simulations it was not possible to conduct a study with such a complex geometry. Therefore, a small area was selected instead (Figure 6-1). Figure 6-1 Design Modeller computational domain To create the computational domain, a rectangular shape was created around the seabed. A boolean subtract was then used to separate the volume under the geometry and to remain with only the desired computational domain. Named selection are created for each side of the domain: inlet, outlet, top, bottom and sides. Ansys meshing application and CFX will then automatically recognize these regions and apply the correct boundary settings (in CFX-Pre). 13

20 6.2 ANSYS Meshing Within ANSYS Meshing application, there are numerous ways to customize the mesh of the fluid domain. This application offers preferences in terms of physics and solvers: CFD was chosen for physics preference and CFX for the solver. The advantage of v15 is that the mesh could be done in parallel on different threads if the model consists of different parts. There is a choice between structured and unstructured mesh. For this application an overall tetrahedral mesh type was chosen for the whole domain and a hex mesh at the bottom. Ideally, a patch conforming method is good to be used to decrease the element size towards the top of the computational domain where there is less interest and to increase it towards the bottom of the domain. The issue with this type of mesh is the fact that the default settings, when changed, behave as a sizing mesh method and it creates a relatively equal element size throughout the domain. For this reason, the sizing method was used instead with an element size of 2mm. This method provides better consistency throughout the domain. The input data in CFX was provided at every millimeter and it would make sense to increase the element size even further (to avoid interpolation of the results) but this was not done due to computational limitations. Due to the complexity of the geometry, it was not possible to reduce the element size even further without compromising the orthogonal quality of the mesh. For this reason, the trials done with a coarser mesh diverged or returned other errors. Some problems were, however encountered when trying to create a mesh for the whole area. Due to very complex geometry, the mesh code struggled to create consistency in the fluid domain. When trying to create a coarse mesh, even though the element size was inputted, the final element size was way bigger that the desired one. Alternatively, when a fine mesh was to be created, due to computational limitations, the computer crushed. Figure 6-2 Computational domain mesh 14

21 To best analyse the turbulence effects above the seabed, an inflation layer should be created on the surface of the geometry. This is essential for calculating the flow separation from the wall when κ-ω SST turbulence or other wall functions are used. For this mesh, 30 layers were created with a growth rate of 1.01 (Figure 6-2). The mesh did not represent the geometry correctly. The reason for this is that, even though small element size was used, the inflation layer failed to create horizontally structured mesh as it is intended to do. Figure 6-3 shows a cross-sectional view of the mesh and it can be easily seen the mesh s non-regularity. The element size is 2 millimetres, but there are areas where significant changes in geometry occur within a smaller distance. This could be the reason why ANSYS would prefer even a smaller element size. Figure 6-3 Computational domain mesh - cross section view 6.3 CFX-Pre: Boundary Conditions The flow parameters at the boundary of the computational domain need to be specified so that these can be used to calculate the flow parameters for each fluid element within the mesh. The main three options are inlet, outlet and wall. Before the boundary conditions (BC) are set up, the type of analysis was selected to steady state and the fluid domain parameters were specified. Here is where the fluid properties are inputted and the turbulence type is set up. For this simulation, three turbulence models were selected: κ-ɛ, κ-ω SST and Reynolds model RSM SMC-BSL with turbulence intensity T i and turbulence length T L as input values. 15

22 The average value of the T i was used from the experimental data (0.01). A sensitivity analysis was conducted for all three turbulence models where the fractional intensity varied from 0.01 to 0.03, 0.05 and 0.1 and the T L varied from 35mm to 15 with increments of 10, while the sand grain roughness remained the same. ANSYS parametrisation is a useful way to conduct the what-if analysis where Design Points could be defined, but for this simulation, the Workbench constantly failed to update the data, hence the simulations had to be done manually. Inflow BC will only allow the fluid to pass into the domain. The inlet velocity was set up according to the Cartesian velocity components measured during the experiment. Outlet BC only allow the fluid to flow out of the computational domain but the opening BC will allow the fluid to flow out and back into the domain. As the fluid tended to flow back into the domain, the opening option was used with pressure settings for the outflow. The bottom BC is set to be wall with no-slip condition. The sand grain roughness of the wall is inputted as Workbench parameter and the value used is an average value for cement: 1.5mm (Texas University, n.d.). To the sides, a wall condition is assigned, but with free slip wall option. This will not enforce a zero normal gradient to all parameters as in the symmetry case. ANSYS CFX simulates the slip by using a moving wall. Finally, the top BC is computed as opening with opening pressure Figure 6-4. Figure 6-4 Boundary Conditions in CFX-Pre 6.4 Main solver The CFX Solver uses an iterative method to calculate the relevant discretized PDEs (Casey & Wintergerste, 2000). Assuming that the model is converging, each iteration takes the data closer to the model solution. The model is usually set to run a number of iterations or until the residuals (the difference between the actual and the exact value) reaches a specific value. For this analysis the 16

23 number of iterations was set to 200, and the residual value to To decrease the simulation time, the initial values were taken from a laminar case and hydrostatic pressure was used. To ensure more accurate numerical mathematical operations, double precision option was selected. This setting determines the default precision of the partitioner, solver, and interpolator executables. It is recommended to be used when the computational domain involves huge variation in grid dimension, pressure range etc (ANSYS CFX, 2013). A velocity-pressure coupling option is selected to Rhie Chhow option, the default forth order. This arrangement provides a strong coupling between the velocities and pressure which helps to avoid some types of convergence problems and oscillations in the pressure and velocity fields (Tu, et al., 2013). Computation resource (both RAM and CPU) is a critical key in developing a numerical study, but there is no algorithm which calculates the exact power needed for a specific simulation. It is generally agreed that for each one million of elements, one GB of RAM is required, but more reliable algorithm is needed to predict the computational power. RESULTS This section presents the measurements taken during the experiment and data from the numerical analysis. 7.1 Experimental data Initially, measurements had to be taken to measure the mean velocity at the centre of the flume at different motor powers. This is essential in order to have a motor power flume velocity correlation. For a velocity of 0.32m/s as presented in the Section 5.2, the motor power required is 29.4%. Figure 7-1 Velocity vs. motor power 17

24 Another set of measurements were taken for a vertical profile on a flat bed, before the bathymetry. As presented in Figure 7-2, there is little vertical variation of the horizontal velocity. The gap in data is either represented by a low correlation between the four beams, a high Signal to Noise Ratio (SNR) or a weak point. Initially, this data was meant to be used as input in the computational domain, but due to computational limitations, a smaller domain was used with its equivalent velocity input. The VP software creates an individual file for each point-measurement. It is therefore essential to merge the results into one file and then to process the data. Two Matlab codes were written by Halswell (2015) to facilitate data analysis: one for merging the point-measurements and the other one to visualize the data. Additional code was written to plot the bathymetry profile and the velocity data on the same figure. Before the data was plotted, the low correlation and high SNR data was removed. Figure 7-2 Vertical inlet velocity profile The main set of measurements were taken across the whole domain and a small, high resolution area. Figure 7-3 presents the full scale velocity across the whole domain data measured on a 18

25 horizontal plane. Due to the lack of reliable depth data, the bottom distance was measured. Unfortunately, the VP failed to record reliable measurements: half of the data was within a reasonable range, but the other half was far beyond the expected value. Another alternative for bottom distance was to use the point cloud data, but in this case, interpolation had to be done for the point of interest. As huge variation of geometry could be identified within a small distance, this method did not prove to be safe. If the instrument hits the surface, then damage may occur. As a consequence, a horizontal plane was used for all measurements so that the first 15mm would be above the highest point of the bathymetry and the last 20mm would be below it. Figure 7-3 Velocity profile across the whole domain Figure 7-4 Velocity profile across the whole domain - zoom in 19

26 Figure 7-3 shows areas where the rate of change is not significant and the velocity tends to be consistent, but Figure 7-4, shows clearly how the velocity changes as a result of the bathymetry effect. Closer to the surface, the velocity decreases and then increases with height. Another set of data was recorded at a much higher resolution (6mm) but due to the density of the data, it is visually not well represented. More information on individual axis velocity, turbulence fluctuation, turbulence intensity, data correlation, amplitude, SNR and data quality could be found in Appendix B. For validation and input into the CFD model, a very small area was chosen due to computational limits. This are is away from the wall boundary effects and the input data could be taken nearly from the bottom level upwards. The input velocity was taken from the first profile in the Figure 7-5. Figure 7-5 Velocity profile for the computational domain 7.2 CFD data The advantage of CFD is that it could estimate the value of different variables in spatial-temporal domains where data is missing. Figure 7-6 Vector velocity plot - CFD 20

27 Figure 7-6 shows the velocity field at the plane where the velocity was taken from the experimental data (Figure 7-5). As shown in both figures, the velocity profile follows the same trend: as expected, very low velocity at the bottom with an increase towards the top. Figure 7-7 shows the velocity distribution at 5mm above the seabed. The high values correspond to high slopes and the area which does not show velocity variation is covered by bathymetry. Figure 7-7 Velocity variation 5mm above seabed - CFD The main data exported from the CFD simulations are point-measurements which correspond to the plane where the input velocity was taken from (Figure 7-5). Twelve points were selected in total, exporting the velocity u in x direction. The location of the points is presented in Table 7-1. Table 7-1 Validation points location ID x y z VALIDATION The data from the twelve selected points was compared against all cases of the numerical simulation. The difference between the selected points (numerical and experimental) was used to quantify how well the data correlates. The RSQ-eq was calculated for each case. Figure 8-1 to 8-3 show the difference for all three turbulence models with the default settings of T i (0.01) and T L (35mm). 21

28 As shown in the graphs, the discrepancy between data follows the same pattern for all three scenarios. Nonetheless, the RSQ-eq shows the difference between them: the κ-ω SST turbulence model shows the lowest discrepancy between the data and the Reynolds model presents the highest one. Figure 8-1 Experimental and CFD data comparison: κ-ɛ Figure 8-2 Experimental and CFD data comparison: κ-ω SST 22

29 Figure 8-3 Experimental and CFD data comparison: RSM SMC-BSL Individual RSQ-eq were calculated for each case, where T i and T L varied. It is interesting to find out how turbulence eddy length scale impact the final RSQ-eq. For each of the eddy length scale considered, the RSQ-eq was plotted for different intensity rates and turbulence models (Figure 8-4 to 8-6). For all three scenarios, the pattern is similar: the lowest RSQ-eq was found for the κ-ω SST turbulence model and the highest for the Reynolds turbulence model. The alphabetic character relates to the turbulence model whereas the numerical one to the T i a comma would be required after the first numerical character (full data is presented in Appendix C - Experiment and CFD data). Figure 8-4 Residual sum of square - eddy length scale 35mm 23

30 Figure 8-5 Residual sum of square - eddy length scale 25mm Figure 8-6 Residual sum of square - eddy length scale 15mm As mentioned previously, the κ-ɛ model predicts the onset of flow separation too late and underpredicts the amount of separation later on. It also involves the complex nonlinear damping functions and has an inability to handle low turbulent Re computations, therefore there are limitations in terms of flow separation. Even though the scalable wall functions allow solution on arbitrarily fine near wall grids, which is a significant improvement over standard wall functions, the model is not applicable for flows with boundary layer separation and flows over curved surfaces. The Reynolds model is characterized by higher degree of universality, but the increased number of transport equations leads to reduced numerical robustness and it tends to be more suitable to complex flows. Even though RSM SMC-BSL model was used, which integrates more source terms than κ-ɛ models and uses eddy turbulent frequency instead of eddy dissipation rate, it proves to be inferior to two-equation models. The κ-ω SST model is designed to bring more accuracy in the flow separation prediction. The code involves near-wall treatment for low-re and it proves to be more accurate and more robust. This allows for a smooth shift from low-re and it is recommended for high accuracy in boundary layer simulations. 24

31 The results show a clear consistency for the same turbulence model and T i when the T L is varied. This means that there is very little variation in the numerical data. Even though the computational domain was carefully selected in order to present variation in the fluid flow, substantial changes in the T L and T i need to be done in order to have more comparative results. This consistency could also be affected by the size of the computational domain. Within a small volume, the effect of the turbulence variables it is not easy to be understood and quantified. For this analysis, the κ-ω SST model is preferred over the other two. This ensures that near wall treatment is carefully analysed and it has the capability to predict the flow separation in a more successful way. 9 ASSUMPTIONS AND LIMITATIONS As in every engineering application, the writer has encountered various assumptions and limitations that need to be addressed in order to better understand and quantify the reliability of the results. These are presented in three categories, as follows: Before the experiment 1. Software limitations to create surface. Various software packages (e.g. SoidWorks, Rhinoceros, ANSYS Design Modeller) offer the capability of creating a surface from a point cloud. However, it is not an easy task to understand the inter and extrapolation codes behind the GUI. Even though packages like RhinoTerrain create a very fine mesh, the software struggles to create the surface from mesh, therefore there will be a discrepancy between them. 2. Exporting IGS file to STL. Little understanding is known about these types of files and how well the geometric data is stored and converted among them. 3. CNC Router: no calibration was made before usage. This could indicate that the physical model may differ from the CAD model. During the experiment 4. Alignment with the CAD model. It was significantly hard to accurately align the physical model in the flume and to identify a precise local home as a point of reference for the home position of the VP and the CAD model. The flume was filled with water and the instrument could not go down, reaching the bathymetry surface. Therefore, this was visually done. 5. Velocity fluctuation in the flume. The inlet velocity used as input for the numerical model fluctuated over time and the value taken was only a time-average value. 6. VP can only measure velocity as close as 3-4mm from a solid boundary (Nortek As, 2013). CFD 7. The analysis type was steady state, therefore only time-average values were considered from the experimental data, instead of time-dependent data. 25

32 8. Model errors. Particularity for turbulence modelling, an error occurs due to simplification of the governing equations which are unable to account for the instantaneous fluctuations of the turbulent flow (Tu, et al., 2013). 9. Truncation and discretization errors - occur when an iterative method is terminated or when a mathematical procedure is approximated and the approximated value differs from the solution. 10. Application uncertainty. This simulation does not consider any effect of the fluid flow outside the computational domain which may affect the results. 10 GUIDELINES This section outlines the main guidelines for the actual application based on theory, other user s and the writer s experience. Before the experiment 1. Bathymetry selection methodology. A very complex and curved geometry will create many challenges during later stages, therefore, a less curved seabed would be recommended. This may involve a smaller scaling factor or a seabed with a smaller rate of change in geometry over a standard area. 2. CAD Software for creating the surface. Amongst the CAD software, Rhinoceros was found to be the most suitable with two useful plug-ins: RhinoTerrain and Resurf. RhinoTerrain has an outstanding build-in mesh code and Resurf has various surface creation capabilities. 3. CNC router machine is recommended to be calibrated before milling. 4. It is advisable to set the home location of the VP in the same place where the home location of the bathymetry is. At the same time it is important to have accurate measurements to set up the home location at the most accurate standard. To avoid reading errors, the flume needs to be drained. During the experiment 5. The water in the flume needs to be filtered from unwater particles which may affect the measurements. 6. Before taking measurements, one needs to ensure that the flow is consistent and it runs as expected. 7. The sealing particles in the water need to be constantly checked. If the SNR is not appropriate, this may indicate that more or less sealing particles are required. 8. The height at which the measurements are taken needs to be carefully considered in order to avoid collision between the instrument and surface. 9. It is recommended to check the location where data needs to be recorded by running the VP through all points of interest. 10. Weak spots need to be avoided by changing the velocity range. 26

33 11. The recorded data needs to be constantly monitored and checked in order to avoid recording unnecessary/unreliable data. CFD Geometry 12. CFD programs require a clean geometry profile. Very complex and curved geometries must be avoided as these require a high resolution mesh and increase the computational intensity of the model but the accuracy is not necessarily improved. If this could not be achieved, then a smaller scaling factor needs to be considered. 13. The size of the enclosure/rectangular area around the bathymetry needs to be slightly smaller than the surface itself in order to create the Boolean subtract operation. Additionally, it is important to create straight edges in order to avoid geometry errors. 14. The computational domain needs to be sized so that it will be large enough that the boundaries would not interfere with the flow in the main area of interest. As no standard is available, best practice from the tidal industry energy could be a starting point (Furlepa, 2015). Mesh 15. The required resolution and the most suitable mesh type is different at different points throughout the domain. Generally speaking, a growth rate needs to be used to decrease the mesh towards the top. Alternatively, if this could not be achieved, the model could be divided into different parts and different mesh could be applied. 16. The curvature of the geometry could be an indication of the initial resolution (ICEM CFD, 2013). 17. High resolution mesh is required to capture the flow separation from wall boundaries. It is important to align the grid lines with the flow to avoid discretization errors (Zigh & Solis, 2013) which could be achieved through inflation layers. 18. Good practice considers appropriate to generally use at least layers (LEAP CFD, 2012). 19. The first layer thickness parameter is important as this is directly proportional with y + value and could be calculated by Δy 1 = 2 y+ μ C f ρ U2 where Cf is empirically estimated as 0.058*Re-0.2 (LEAP CFD, 2013). 20. It is important to check the mesh quality. The included angles should be between 40 and 140 degrees and around the wall boundaries as close to 90 degrees as possible (Tu, et al., 2013). 27

34 CFX-Pre 21. Mesh adaption option could be selected to adapt the mesh as it solves if the code detects weak grid. 22. The κ-ω SST turbulence model is recommended to be used for better accuracy for the flow separation. The Ti, TL or other turbulent parameters need to be selected and this tend to be site/application specific. 23. The BCs need to be carefully selected to replicate the physical domain. The inflow BC needs to have reliable experimental data such as Cartesian velocities and turbulence parameters (usually Ti and TL) and the outlet (opening) BC is recommended to have a weak effect on the upstream flow. The wall roughness must be specified with care as this could introduce uncertainty. A sensitivity analysis is recommended if the wall roughness could not be calculated. Validation 24. A high number of data points need to be measured across the domain in order to avoid as much uncertainty as possible. Also, consideration of many variables must be taken in order to avoid errors associated with some variables but not with others. 25. The numerical data must be compared against filed measurements and statistical methods could be used for field data. 26. Statistical tools may be used to quantify the validation and to keep a level of consistency in the method. 11 FURTHER WORK The actual investigation of the turbulence effects could be further investigated and more levels of complexity could be added. The main improvements are presented as follows: 1. More investigation into ANSYS parametrization is required. For this analysis the software failed to automatically update the design points. 2. More robust validation methodologies such as validation metrics are required. Confidence intervals to describe probability of the difference between the experimental mean and the computational result are desirable. 3. An advanced sensitivity analysis would bring more insight into the topic. This could investigate various BC, wall roughness, turbulence parameters and the sensitivity of different CFD codes. 4. The project assets such as the turbines could be incorporated in the analysis. These would create additional turbulence and it is good to quantify it. 5. To replicate real flow characteristics, a flume with multiple flow directions is required. The input data must be from field measurements and in this way, three way validation could be done. 28

35 6. In addition to point 5, wave effects on the seabed could be investigated in a wave tank. Beside the linear wave theory, it is interesting to find out more about the effect of wave and current interaction with various scenarios. 7. More understanding on the surface creation codes is required in order to quantify the limitations at this stage. NURBS generation could be very problematic for CFD modelling and good understanding of the interpolation and extrapolation functions is required. 8. The distance to the surface must be known in order to follow the bathymetry profile while recording data. This could be achieved by investigating point 7 or an instrument could be used with better bottom-check functions. This would enable safe movement of the instrument and will avoid collision on the neighboring bathymetry profile. 9. A thorough analysis of the sheltering effects on the seabed where parametrization could be used to quantify the effect of various shapes of the profile on the subsea cables where angles and slopes could potentially define the flow variation. This advanced approach may significantly change the industry approach to this topic. 29

36 12 CONCLUSION The offshore cables for the marine renewables industry still remain a main area of concern due to the fatigue and cable stability issues. Up to this stage, the industry is lacking significant experience in dealing with these challenges and the need for smart routing techniques is essential. The cable software is designed to meet this need, but more studies on guidelines on CFD modelling as input data are required. This report could be used as initial step for developing comprehensive best practice. Limited documentation was specifically found for offshore cables in the renewable industry. Studies on submarine pipelines and sediment transport show that κ-ɛ turbulence model is widely used and κ-ω provides better results for near wall applications. However, these seem to be application and site specific. More studies need to be done using the bathymetry instead of flat beds. The experimental trials have successfully run and the velocity profiles show the effect of the bathymetry on the flow. The actual model is a simplification in terms of similarity as Reynolds and Froude similarity cannot be attained simultaneously. The complexity of the curved geometry proved to be an issue for the mesh generation. Different approaches have been applied, with the sizing and inflation method used in the end. Due to limitations in computational power, a mesh for the initial computational volume could not be achieved. However, a smaller computational volume was selected in order to conduct a comparison study. More research is required for determining an algorithm that predicts the computational power. The validation technique in this analysis uses RSQ-eq and the results show that κ-ω SST model has the lowest discrepancy between the numerical and experimental data. There is little variation for RSQ-eq value when the same turbulence model and fractional intensity is used but the turbulent length scale differs. Different validation methodologies are recommended to be used in order to increase the confidence level in the validation approach. Validation metrics with confidence intervals could be implemented and data from a wide range of locations and different variables should be considered. 30

37 13 BIBLIOGRAPHY Ali, A., Sharma, R., Ganesan, P. & Akib, S., Turbulence Model Sensitivity and Scour Gap Effect of unsteady Flow around the pipe: A CFD study. The Scientific World Journal, p. Article ID: ANSYS CFX, The k-epsilon Model. ANSYS CFX User Manual, s.l.: Version ANSYS, ANSYS CFX. [Online] Available at: s/ansys+cfx [Accessed ]. Baston, S. et al., n.d. Sensitivity Analysis of the Turbulence Closure models in the Assessment of Tidal Energy Resource in Orkney, Orkney: ICIT, Institute of Petrolium Engineering; Heriot-Watt University - Orkey Campus. Baumert, H. Z., Simpson, J. H. & Sundermann, J., Marine Trubulence - Theories, Observations and Models. Cambridge: Cambridge University Press. Casey, M. & Wintergerste, T., ERCOFTAC Special Interest Group on "Quality and Trust in Industrial CFD": Best Practive Guidelines, s.l.: Sulzer Innotec. Chang, K.-T. & Jeng, D.-S., Numerical study for wave-induced seabed response around offshore wind turbine foudnation in Donghai offshore wind farm, Shangai, Chian. Ocean Engineering, Volume 85, pp Chapalain, G. & Thais, L., Tide, turbulence and suspended sediment modelling in the eastern English Channel. Coastal Engineering, Volume 41, pp DECC, UK Renewable energy Roadmap, s.l.: s.n. DNV, Free Spanning Pipelines. Recommended Practice: DNV-RP-F105, s.l.: DET NORSKE VERITAS. DNV, Environmental Conditions and Environmental Loads. Recommended Practice: DNV- RP-C205, s.l.: DET NORSKE VERITAS. DNV, Subsea Power Cables in Shallow Watter Renewable Energy Applications. Recommended Practice DNV-RP-J301, s.l.: DET NORSKE VERITAS AS. Furlepa, A., Best Practice Guidelines. Computational Fluid Dynamics for Tidal Stream Turbine Application, s.l.: s.n. Hakan, G., Introduction to Turbulence, Luleå University of Technology: s.n. Halswell, P., Matlab codes: MakeVPStructure; Matlab codes: Visualise_data;, s.l.: s.n. 31

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40 A. APPENDIX A SCALING LAWS A

41 B. APPENDIX B EXPERIMENTAL DATA GRAPH This section presents experimental data graph for individual velocity axis, turbulence fluctuation, SNR, data quality and correlation. FigureB 1 Full scale X-axis velocities B

42 FigureB 2 Full scale Y-axis velocities C

43 FigureB 3 Full scale Z-axis velocities D

44 The turbulence fluctuation tends to have a higher magnitude at the location where the flow intersects the bathymetry. The graph show a combined, full scale turbulence fluctuation and its direction. FigureB 4 Full scale RMS turbulence fluctuation E

45 This graph shows the full-scale RMS turbulence fluctuation for all axis. FigureB 5 RMS turbulence fluctuation - individual axis F

46 Signal to Noise Ratio measures is a measure of the desired signal to the level of background noise. FigureB 6 Signal-Noise Ratio G

47 Data quality is measured between 0 and 1. If the data is assigned 0, this means that data has a good quality. FigureB 7 Data quality H